Shape Optimization for Stokes Flows using Conformal Metrics | Zendy

Leithäuser Christian | Zendy; Feßler Robert | Zendy; Pinnau René | Zendy

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Shape Optimization for Stokes Flows using Conformal Metrics

Author(s) -

Leithäuser Christian,

Feßler Robert,

Pinnau René

Publication year - 2010

Publication title -

pamm

Language(s) - English

Resource type - Journals

ISSN - 1617-7061

DOI - 10.1002/pamm.201010283

Subject(s) - conformal map , metric (unit) , computation , shape optimization , domain (mathematical analysis) , shear stress , flow (mathematics) , stokes flow , mathematics , geometry , conformal geometry , differential (mechanical device) , differential geometry , mathematical analysis , mathematical optimization , physics , algorithm , mechanics , conformal symmetry , engineering , finite element method , operations management , thermodynamics

We derive a shape optimization approach for a two‐dimensional Stokes flow problem. Our goal is to compute a geometry whose wall shear stress is L 2 ‐close to a desired target stress. Computations are carried out on a fixed domain, while shape variations are described through conformal metric changes. Tools from differential geometry are used to handle metric dependent operators. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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